The main concerns seem to be sweat or the spread of skin infections. However, shirts and rash guards do little to prevent the spread of skin infections, the main preventatives here are checking athletes for signs of infection before competition and good hygiene before and after competition. And sweat soaks right through a shirt or rash guard anyway, but a wet shirt will hold the moisture against your skin and begin to smell much faster.
Others prefer the shirtless uniform for comfort, tradition, or hygiene reasons. And some simply think the choice should be left up to the athlete. One commenter suggested that they should rather ban loose and baggy shirts that may tangle and get in the way during competition.
It is still fairly early as of this writing, so feel free to go and cast your vote on the survey.
(The pictures are actually from another organization, the North America Grappling Association.)
You can vote on the petition here.
You can comment on the related Facebook post here.
U.S. Grappling has actually adopted a rule requiring shirts, in spite of the fact that the majority on their survey voted in favor of keeping shirts optional. There is now a petition you can sign to encourage them to change the rule back. Please sign the petition and share it on Facebook and Twitter. Meanwhile, NAGA has confirmed that they are not requiring shirts.